An extension of an over-dispersion test for count data

While over-dispersion in capture–recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture–recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture–recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

Whole crop cereals 2. Prediction of apparent digestibility and energy value from in vitro digestion techniques and near infrared reflectance spectroscopy and of chemical composition by near infrared reflectance spectroscopy

Samples of whole crop wheat (WCW, n = 134) and whole crop barley (WCB, n = 16) were collected from commercial farms in the UK over a 2-year period (2003/2004 and 2004/2005). Near infrared reflectance spectroscopy (NIRS) was compared with laboratory and in vitro digestibility measures to predict digestible organic matter in the dry matter (DOMD) and metabolisable energy (ME) contents measured in vivo using sheep. Spectral models using the mean spectra of two scans were compared with those using individual spectra (duplicate spectra). Overall NIRS accurately predicted the concentration of chemical components in whole crop cereals apart from crude protein. ammonia-nitrogen, water-soluble carbohydrates, fermentation acids and solubility values. In addition. the spectral models had higher prediction power for in vivo DOMD and ME than chemical components or in vitro digestion methods. Overall there Was a benefit from the use of duplicate spectra rather than mean spectra and this was especially so for predicting in vivo DOMD and ME where the sample population size was smaller. The spectral models derived deal equally well with WCW and WCB and Would he of considerable practical value allowing rapid determination of nutritive value of these forages before their use in diets of productive animals. (C) 2008 Elsevier B.V. All rights reserved.

Conservation ecology of bees: populations, species and communities

Recent concerns regarding the decline of plant and pollinator species, and the impact on ecosystem functioning, has focused attention on the local and global threats to bee diversity. As evidence for bee declines is now accumulating from over broad taxonomic and geographic scales, we review the role of ecology in bee conservation at the levels of species, populations and communities. Bee populations and communities are typified by considerable spatiotemporal variation; whereby autecological traits, population size and growth rate, and plant-pollinator network architecture all play a role in their vulnerability to extinction. As contemporary insect conservation management is broadly based on species- and habitat-targeted approaches, ecological data will be central to integrating management strategies into a broader, landscape scale of dynamic, interconnected habitats capable of delivering bee conservation in the context of global environmental change.

Measuring the functional responses of farmland birds: an example for a declining seed-feeding bunting

1. Many farmland bird species have undergone significant declines. It is important to predict the effect of agricultural change on these birds and their response to conservation measures. This requirement could be met by mechanistic models that predict population size from the optimal foraging behaviour and fates of individuals within populations. A key component of these models is the functional response, the relationship between food and competitor density and feeding rate. 2. This paper describes a method for measuring functional responses of farmland birds, and applies this method to a declining farmland bird, the corn bunting Miliaria calandra L. We derive five alternative models to predict the functional responses of farmland birds and parameterize these for corn bunting. We also assess the minimum sample sizes required to predict accurately the functional response. 3. We show that the functional response of corn bunting can be predicted accurately from a few behavioural parameters (searching rate, handling time, vigilance time) that are straightforward to measure in the field. These parameters can be measured more quickly than the alternative of measuring the functional response directly. 4. While corn bunting violated some of the assumptions of Holling's disk equation (model 1 in our study), it still provided the most accurate fit to the observed feeding rates while remaining the most statistically simple model tested. Our other models may be more applicable to other species, or corn bunting feeding in other locations. 5. Although further tests are required, our study shows how functional responses can be predicted, simplifying the development of mechanistic models of farmland bird populations.

The relationship between multi-species catch and effort: among fishery comparisons

The control of fishing mortality via fishing effort remains fundamental to most fisheries management strategies even at the local community or co-management level. Decisions to support such strategies require knowledge of the underlying response of the catch to changes in effort. Even under adaptive management strategies, imprecise knowledge of the response is likely to help accelerate the adaptive learning process. Data and institutional capacity requirements to employ multi-species biomass dynamics and age-structured models invariably render their use impractical particularly in less developed regions of the world. Surplus production models fitted to catch and effort data aggregated across all species offer viable alternatives. The current paper seeks models of this type that best describe the multi-species catch–effort responses in floodplain-rivers, lakes and reservoirs and reef-based fisheries based upon among fishery comparisons, building on earlier work. Three alternative surplus production models were fitted to estimates of catch per unit area (CPUA) and fisher density for 258 fisheries in Africa, Asia and South America. In all cases examined, the best or equal best fitting model was the Fox type, explaining up to 90% of the variation in CPUA. For lake and reservoir fisheries in Africa and Asia, the Schaefer and an asymptotic model fitted equally well. The Fox model estimates of fisher density (fishers km−2) at maximum yield (iMY) for floodplain-rivers, African lakes and reservoirs and reef-based fisheries are 13.7 (95% CI [11.8, 16.4]); 27.8 (95% CI [17.5, 66.7]) and 643 (95% CI [459,1075]), respectively and compare well with earlier estimates. Corresponding estimates of maximum yield are also given. The significantly higher value of iMY for reef-based fisheries compared to estimates for rivers and lakes reflects the use of a different measure of fisher density based upon human population size estimates. The models predict that maximum yield is achieved at a higher fishing intensity in Asian lakes compared to those in Africa. This may reflect the common practice in Asia of stocking lakes to augment natural recruitment. Because of the equilibrium assumptions underlying the models, all the estimates of maximum yield and corresponding levels of effort should be treated with caution.

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Nest spacing and breeding performance in Short-toed Eagle Circaetus gallicus in northeast Greece

Aims: To describe the phenology and breeding success of one of the densest populations of Short-toed Eagle in Europe. Methods All nests in the Dadia-Lefkimi-Soufli forest in northeast Greece were located and visited regularly throughout the 1996-98 breeding seasons. Data on every stage of the breeding cycle were collected and related to among-year variation in the weather conditions during March to June. Results: A total of 58 pairs were located during the three-year study spread across 22 territories (the same territories are usually occupied each year). The nests were evenly spaced (mean of 2.7 km between nests). Adults arrived between mid-March and mid-April. Only one egg per nest was laid. Nestlings fledged on average after 68.9 days. Eagles departed between 8 September and 2 October. Conclusions: Arrival date determines laying date. The population size appears to be stable but the species has a relatively low reproductive rate and takes three to four years to mature, consequently it may be susceptible to stochastic or human-mediated factors.

On the regulation of populations of mammals, birds, fish, and insects

A key unresolved question in population ecology concerns the relationship between a population's size and its growth rate. We estimated this relationship for 1780 time series of mammals, birds, fish, and insects. We found that rates of population growth are high at low population densities but, contrary to previous predictions, decline rapidly with increasing population size and then flatten out, for all four taxa. This produces a strongly concave relationship between a population's growth rate and its size. These findings have fundamental implications for our understanding of animals' lives, suggesting in particular that many animals in these taxa will be found living at densities above the carrying capacity of their environments.

Conserving marginal populations of the foodplant (Impatiens noli-tangere) of an endangered moth (Eustroma reticulatum) in a changing climate

Impatiens noli-tangere is scarce in the UK and probably only native to the Lake District and Wales. It is the sole food plant for the endangered moth Eustroma reticulattum. Significant annual fluctuations in the size of I. noli-tangere populations endanger the continued presence of E. reticulatum in the UK. In this study, variation in population size was monitored across native populations of L noli-tangere in the English Lake District and Wales. In 1998, there was a crash in the population size of all metapopulations in the Lake District but not of those found in Wales. A molecular survey of the genetic affinities of samples in 1999 from both regions and a reference population from Switzerland was performed using AFLP and ISSR analyses. The consensus UPGMA dendrogram and a PCO scatter plot revealed clear differentiation between the populations of L noli-tangere in Wales and those in the Lake District. Most of the genetic variation in the UK (H-T= 0.064) was partitioned between (G(ST) = 0.455) rather than within (H-S = 0.034) regions, inferring little gene flow occurs between regions. There was similar bias towards differentiation between metapopulations in Wales, again consistent with low levels of interpopulation gene flow. This contrasts with far lower levels of differentiation in the Lake District which suggests modest rates of gene flow may occur between populations. It is concluded that in the event of local extinction of sites or populations, reintroductions should be restricted to samples collected from the same region. We then surveyed climatic variables to identify those most likely to cause local extinctions. Climatic correlates of population size were sought from two Lake District metapopulations situated close to a meteorological station. A combination of three climatic variables common to both sites explained 81-84% of the variation in plant number between 1990 and 2001. Projected trends for these climatic variables were used in a Monte Carlo simulation which suggested an increased risk of I. noli-tangere population crashes by 2050 at Coniston Water. but not at Derwentwater. Implications of these findings for practical conservation strategies are explored. (C) 2003 Elsevier Ltd. All rights reserved.

Dynamics and foraging behaviour of adult hornet robberflies, Asilus crabroniformis: implications for conservation strategy

Mark resighting studies of the hornet robberfly, Asilus crabroniformis, were carried out during the flight seasons of 1999 and 2000 on agricultural land on the Chilterns in Oxfordshire, UK. Six patches of land were identified which contained characteristics thought to be attractive to hornet robberflies. One hundred and twenty eight adults were marked in 1999 and 257 in 2000. Marking was carried out on one of the patches, but resighting observations were collected from all six sites. The daily population sizes were estimated using the Jolly-Seber method. The daily population size peaked between 50 and 72 from 23 August until 13 September in 2000. This was very similar to the peak population size of between 50 and 74 estimated for 1999. Adults were found to be capable of living for nearly 5 weeks. The maximum linear distance from the point of marking that any individual moved across the study site was 625 m, but some individuals moved over 400 m in a single day. Unsuitable habitat (suburban gardens and a main road) did not present a barrier to dispersal. Males were more likely than females to loiter in sites peripheral to the breeding site, whilst females seemed to be more tied to the breeding site. Most adults were caught from dung piles, but insects avoided fresh dung and preferred instead dung that was well into the process of drying out. A variety of insect species were taken as prey, including many beetles and flies. The findings of the study are discussed in relation to the management of the landscape to enhance the long-term prospects of the hornet robberfly in the UK, and to achieve the UK Biodiversity Action Plan target for this species.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Physical interpretation of the spectral radiative signature in the transition zone between cloud-free and cloudy regions

One-second-resolution zenith radiance measure- ments from the Atmospheric Radiation Measurement pro- gram’s new shortwave spectrometer (SWS) provide a unique opportunity to analyze the transition zone between cloudy and cloud-free air, which has considerable bearing on the aerosol indirect effect. In the transition zone, we find a re- markable linear relationship between the sum and difference of radiances at 870 and 1640 nm wavelengths. The intercept of the relationship is determined primarily by aerosol prop- erties, and the slope by cloud properties. We then show that this linearity can be predicted from simple theoretical con- siderations and furthermore that it supports the hypothesis of inhomogeneous mixing, whereby optical depth increases as a cloud is approached but the effective drop size remains un- changed.

Extending the Lincoln–Petersen estimator for multiple identifications in one source

The Lincoln–Petersen estimator is one of the most popular estimators used in capture–recapture studies. It was developed for a sampling situation in which two sources independently identify members of a target population. For each of the two sources, it is determined if a unit of the target population is identified or not. This leads to a 2 × 2 table with frequencies f11, f10, f01, f00 indicating the number of units identified by both sources, by the first but not the second source, by the second but not the first source and not identified by any of the two sources, respectively. However, f00 is unobserved so that the 2 × 2 table is incomplete and the Lincoln–Petersen estimator provides an estimate for f00. In this paper, we consider a generalization of this situation for which one source provides not only a binary identification outcome but also a count outcome of how many times a unit has been identified. Using a truncated Poisson count model, truncating multiple identifications larger than two, we propose a maximum likelihood estimator of the Poisson parameter and, ultimately, of the population size. This estimator shows benefits, in comparison with Lincoln–Petersen’s, in terms of bias and efficiency. It is possible to test the homogeneity assumption that is not testable in the Lincoln–Petersen framework. The approach is applied to surveillance data on syphilis from Izmir, Turkey.